Laws of large numbers, uncorrelation, and convergence of weighted sums of random variables

1978 ◽  
pp. 44-70
Author(s):  
Robert L. Taylor
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Sums Of Random Variables ◽  
Large Numbers

scholarly journals A note on convergence of weighted sums of random variables

1985 ◽  
Vol 8 (4) ◽  
pp. 805-812 ◽  
Author(s):  
Xiang Chen Wang ◽  
M. Bhaskara Rao
Keyword(s):  
Integrability Condition ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Uniform Integrability ◽  
Laws Of Large Numbers ◽  
Sums Of Random Variables ◽  
Large Numbers ◽  
Pairwise Independent Random Variables ◽  
Weak Laws

Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.

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